Optical sheet, backlight and liquid crystal display apparatus

ABSTRACT

An optical sheet has a large number of cylindrical lens elements provided successively on one of principal faces thereof. The cylindrical lens elements have a finite focal distance on the emission side of illumination light and have an aspheric face of a leftwardly and rightwardly symmetric sectional shape. Where a Z axis is taken in parallel to a normal line direction to the optical sheet and an X axis is taken in a direction of the row of the cylindrical lens elements, a cross sectional shape of the cylindrical lens elements satisfies
 
 Z=X   2 /( R +√{square root over ( )}( R   2 −(1 +K ) X   2 ))+ AX   4   +BX   5   +CX   6 + . . .
         (where R is the radius of curvature of a distal end vertex, K is a conic constant, and A, B, C, . . . are aspheric coefficients).

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority to Japanese Patent Document No.P2004-288518 filed on Sep. 30, 2004, the disclosure of which is hereinincorporated by reference.

BACKGROUND

This invention relates to an optical sheet for enhancing the directivityof light and a backlight and a liquid crystal display apparatus whichinclude the optical sheet.

BACKGROUND ART

In recent years, to a liquid crystal display apparatus which includes aliquid crystal panel, it is a significant subject to enhance the displayluminance together with reduction of the power consumption in order toraise the commodity value of the liquid crystal display apparatus. Insuch a situation as just described, it is demanded strongly to improvethe optical gain on the backlight side. Thus, it has been proposed, as amethod which satisfies the demand, to provide a liquid crystal displayapparatus with a prism sheet which includes a prism array on theemitting side of illumination light (refer to, for example, JapanesePatent No. 3147205).

FIG. 1 shows an external appearance of a conventional prism sheet. FIG.2 shows a shape of an XZ section of the conventional prism sheet. Theprism sheet can separate an incident light ray into a first-ordertransmission light component T1 which is transmitted directly through aprism lateral face, a return light component R which is reflected by theprism lateral face and then reflected by the other prism lateral face sothat it is returned to the incidence side, and a second-ordertransmission light component T2 which is reflected by the prism lateralface and then transmitted through the other prism lateral face so thatit is emitted to a front face of the prism sheet depending upon theincident angle.

The first-order transmission light component T1 is a light fluxcomponent which includes light emitted in a front face direction and isutilized effectively. The return light component R is a light fluxcomponent which enters and is diffused and reflected by the diffusionsheet, which is regarded as a light emitting face (planar light source),and is effective to increase the luminance of the light emitting face.The second-order transmission light component T2 is a light fluxcomponent which is emitted to the wide angle side outside an effectiveangular field of view of the liquid crystal panel and does notcontribute to enhancement of the luminance.

In this manner, the conventional prism sheet refracts and transmitsincident light therethrough to condense the incident light in the frontface direction thereby to improve the directivity characteristic so asto increase the front face luminance. Further, since reflected light isdiffused and scattered by the diffusing sheet which is regarded as alight emitting face (planar light source) to increase the luminance ofthe light emitting face, the front face luminance increases.

As described above, the conventional prism sheet can separate anincidence light ray into one of the first-order transmission lightcomponent T1, second-order transmission light component T2 and returnlight component R depending upon the incidence angle of the incidencelight.

In the conventional prism sheet, as seen in FIG. 2, part of a light fluxemitted from an off-axis imaginary light source is totally reflected byone of lateral faces of the prism sheet and re-enters the other lateralface, whereafter it advances in the inside of the sheet and isre-utilized as the return light component R. Or, the part of the lightflux is effectively utilized, after multiple reflections thereof, as thefirst-order transmission light component T1 or as the return lightcomponent R to the light source side.

However, some light flux emitted from an off-axis imaginary light sourceis totally reflected by one of lateral faces of the prism sheet and thenis refracted by and transmitted through the other lateral face so thatit makes the second-order transmission light component T2 which isemitted to the wide angle side outside the effective angular field ofview of the liquid crystal panel. The second-order transmission lightcomponent T2 is a light flux component which is ineffective toimprovement of the luminance.

Further, depending upon the angle dependent characteristic of apolarized light separation sheet disposed on the succeeding stage,extreme deterioration of the polarized light separation characteristicis sometimes caused by the directivity of incident light, which makes anobstacle to effective luminance enhancement to the liquid crystal panelside.

Further, where the prism sheet described above is interposed between adiffusing sheet and a liquid crystal panel, external appearance blurringappears. Therefore, it is demanded to suppress occurrence of externalappearance blurring.

SUMMARY

Accordingly, it is a first object of the present invention to provide anoptical sheet which implements a high luminance distribution within apredetermined angular field of view and can suppress appearance of asecond-order transmission light component T2 to enhance the luminanceand a backlight and a liquid crystal display apparatus which include theoptical sheet.

It is a second object of the present invention to provide an opticalsheet which implements a high luminance distribution within apredetermined angular field of view and can suppress appearance of asecond-order transmission light component T2 to enhance the luminanceand besides can suppress, where a prism sheet is provided between adiffuser and a liquid crystal panel, appearance of external appearanceblurring and a backlight and a liquid crystal display apparatus whichinclude the optical sheet.

The inventor of the present invention has studied hard in order to solvethe subjects described above which the prior art has. An outline isdescribed below.

According to the knowledge of the inventor of the present invention,with a conventional prism sheet, some second order transmission lightenters an adjacent prism and hence re-enters the inside of the sheet,and consequently is added to and re-utilized together with return light.Further, some second order transmission light is effectively utilized asfirst order transmission light or return light to the light source sideafter multiple reflection. In contrast, some second order transmissionlight, so-called side robe light, is not utilized effectively. Most ofsuch second order transmission lights are generated when light incidentfrom an oblique direction with respect to a principal surface of a prismsheet is totally reflected by one of faces of a prism and then refractedby and transmitted through the other face of the prism.

Further, according to the knowledge of the inventor, light incident on aportion of the prism in the proximity of a vertex from a directionperpendicular to the principal face of the prism sheet is totallyreflected, and therefore, the first order transmission light decreases.

Therefore, the inventor has studied hard with regard to an interfacewhich can forwardly refract and transmit light incident on a portion ofa prism in the proximity of a vertex from a direction perpendicular to aprincipal face of a prism sheet to increase the first order transmissionlight while it totally reflects light incident from a direction obliqueto the principal face of the prism sheet at one face thereof and thentotally reflects or refracts and transmits the totally reflected lightat the other face thereof to increase the return light. As a result, theinventor has invented an interface wherein a large number of cylindricallens elements having a hyperboloidal surface or a paraboloidal surfaceare juxtaposed in a direction perpendicular to a generating line of thecylindrical lens elements.

The present invention has been made based on the studies describedabove.

In order to solve the subject described above, according to a firstaspect of the present invention, there is provided an optical sheethaving cylindrical lens elements which have a high-order aspheric faceand are provided successively in a row on one of principal faces of theoptical sheet, characterized in that,

where a Z axis is taken in parallel to a normal line direction to theoptical sheet and an X axis is taken in a direction of the row of thecylindrical lens elements, a cross sectional shape of the cylindricallenses satisfies the following expression:Z=X ²/(R+√{square root over ( )}(R ²−(1+K)X ²))+AX ⁴ +BX ⁵ +CX ⁶+ . . .

(where R is the radius of curvature of a distal end vertex, K is a conicconstant, and A, B, C, . . . are aspheric coefficients.)

According to a second aspect of the present invention, there is provideda backlight, characterized in that the backlight comprises:

a light source for emitting illumination light; and

an optical sheet for raising the directivity of the illumination lightemitted from the light source; that

the optical sheet has, on the illumination light emission side thereof,cylindrical lens elements which have a high-order aspheric face and areprovided successively in a row; and that, where a Z axis is taken inparallel to a normal line direction to the optical sheet and an X axisis taken in a direction of the row of the cylindrical lens elements, across sectional shape of the cylindrical lenses satisfies the followingexpression:Z=X ²/(R+√{square root over ( )}(R ²−(1+K)X ²))+AX ⁴ +BX ⁵ +CX ⁶+ . . .

(where R is the radius of curvature of a distal end vertex, K is a conicconstant, and A, B, C, . . . are aspheric coefficients.)

According to a third aspect of the present invention, there is provideda liquid crystal display apparatus, characterized in that the liquidcrystal display apparatus comprises: a light source for emittingillumination light; an optical sheet for raising the directivity of theillumination light emitted from the backlight; and a liquid crystalpanel for displaying an image based on the illumination light emittedfrom the optical sheet; that the optical sheet has, on the illuminationlight emission side thereof, cylindrical lens elements which have ahigh-order aspheric face and are provided successively in a row; andthat, where a Z axis is taken in parallel to a normal line direction tothe optical sheet and an X axis is taken in a direction of the row ofthe cylindrical lens elements, a cross sectional shape of thecylindrical lenses satisfies the following expression:Z=X ²/(R+√{square root over ( )}(R ²−(1+K)X ²))+AX ⁴ +BX ⁵ +CX ⁶+ . . .

(where R is the radius of curvature of a distal end vertex, K is a conicconstant, and A, B, C, . . . are aspheric coefficients.)

In the first, second and third aspects of the present invention,preferably the radius R of curvature, the conic constant K and theaspheric coefficients A, B, C, . . . satisfy the following numericalranges:

R≧0

K<−1

0<A<10⁻³

0≦B, C . . . <10⁻³

In the first, second and third aspects of the present invention,preferably the radius R of curvature, the conic constant K and theaspheric coefficients A, B, C, . . . satisfy the following numericalranges:

0<R≦72

−15<K≦−1

R−K≧5

0≦A, B, C . . . <10⁻³

4. An optical sheet according to claim 1, characterized in that theradius R of curvature, the conic constant K and the asphericcoefficients A, B, C, . . . satisfy the following numerical ranges:

0<R≦30

−15<K≦−1

R−K≧5

0≦A, B, C . . . <10⁻³

In the first, second and third aspects of the present invention,preferably convex portions having a height equal to or greater than 0.20μm from an average central plane are further provided on the otherprincipal face side opposite to the one principal face on which thecylindrical lens elements are provided, and that the density of theconvex portions is equal to or higher than 70/mm² but equal to or lowerthan 500/mm².

In the first, second and third aspects of the present invention,preferably convex portions having a height equal to or greater than 0.20μm from an average central plane are further provided on the otherprincipal face side opposite to the one principal face on which thecylindrical lens elements are provided, and that the average distancebetween the convex portions is equal to or greater than 50 μm but equalto or smaller than 120 μm.

In the first, second and third aspects of the present invention,preferably convex portions are further provided on the other principalface side opposite to the one principal face on which the cylindricallens elements are provided, and that the convex portions are providedsuch that, in a state wherein the cylindrical lens elements are notformed, the cloudiness degree of the optical sheet is equal to or lowerthan 60%.

In the first, second and third aspects of the present invention,preferably convex portions are further provided on the other principalface side opposite to the one principal face on which the cylindricallens elements are provided, and that the convex portions are providedsuch that, in a state wherein the cylindrical lens elements are notformed, the cloudiness degree of the optical sheet is equal to or lowerthan 20%.

In the first, second and third aspects of the present invention,preferably convex portions are further provided on the other principalface side opposite to the one principal face on which the cylindricallens elements are provided, and that the ten-point average roughness SRzof the convex portions is equal to or higher than 1 μm but equal to orlower than 15 μm.

In the first, second and third aspects of the present invention,preferably convex portions are further provided on the other principalface side opposite to the one principal face on which the cylindricallens elements are provided, and that the height of the convex portionsat which the convex portion area occupies 1% is equal to or greater than1 μm but equal to or smaller than 7 μm.

In the first, second and third aspects of the present invention,preferably convex portions are further provided on the other principalface side opposite to the one principal face on which the cylindricallens elements are provided, and that the average inclination gradient ofthe face on the side on which the convex portions are provided is equalto or greater than 0.25.

In the first, second and third aspects of the present invention, theoptical sheet can refract and transmit light incident from a directionperpendicular to a principal face thereof by a comparatively greatamount to a forward direction. Besides, the optical sheet can totallyreflect light incident from an oblique direction with respect to theprincipal face thereof at one of faces thereof and then totally reflector refract and transmit the totally reflected light at the otherprincipal face to form return light.

Further, since the convex portions are provided on the other principalface on the opposite side to the one principal face on which thecylindrical lens elements are provided, also where the optical sheet isprovided on a diffuser, the optical sheet can be preventing fromadhering to the diffuser.

As described above, according to the present invention, the directivitycan be improved to enhance the front face luminance to achievecontribution to the enhancement of the characteristic by the polarizedlight separation sheet on the succeeding stage. Consequently, thedisplay luminance of the liquid crystal panel can be enhanced togetherwith reduction of the power consumption.

Further, since the second order transmission light flux component T2 tobe emitted to the wide angle is reduced, the front face luminance can beenhanced to achieve contribution to the enhancement of thecharacteristic by the polarized light separation sheet on the succeedingstage. Consequently, the display luminance of the liquid crystal panelcan be enhanced together with reduction of the power consumption.

Further, the incident angle of the illumination light flux to the liquidcrystal panel itself can be controlled to the normal line direction, andthe color separation (blurring in color) on the wide angle side can becontrolled.

Further, since the convex portions are provided on the other principalface on the opposite side to the one principal face on which thecylindrical lens elements are provided, where the optical sheet isprovided in the liquid crystal display apparatus, appearance of externalappearance blurring can be suppressed. Further, since the slidingcharacteristic can be enhanced, appearance of damage to the rear face ofthe lens sheet and to another sheet disposed in an opposing relationshipto the rear face can be suppressed.

Additional features and advantages of the present invention aredescribed in, and will be apparent from, the following DetailedDescription and the Figures.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a perspective view showing an external appearance of a prismsheet;

FIG. 2 is a schematic view showing an XZ section of the prism sheet;

FIG. 3 is a cross sectional view showing an example of a configurationof a liquid crystal display apparatus according to an embodiment of thepresent invention;

FIG. 4 is a perspective view showing an example of a shape of a lenssheet according to the embodiment of the present invention;

FIG. 5 is a schematic view showing an example of a configuration of anextruded sheet precision molding apparatus used in a production methodfor an optical film according to the embodiment of the presentinvention;

FIG. 6 is a schematic view showing part of an XZ section of aconventional prism sheet in an enlarged scale;

FIG. 7 is a distribution diagram illustrating a light distributioncharacteristic of a conventional prism sheet;

FIG. 8 is a distribution diagram illustrating a visual fieldcharacteristic of a conventional prism sheet;

FIG. 9 is a schematic view showing part of an XZ section of a lens sheetof a working example 1 in an enlarged scale;

FIG. 10 is a distribution diagram illustrating a light distributioncharacteristic of the lens sheet of the working example 1;

FIG. 11 is a schematic view showing part of an XZ section of a lenssheet of a working example 2 in an enlarged scale;

FIG. 12 is a distribution diagram illustrating a light distributioncharacteristic of the lens sheet of the working example 2;

FIG. 13 is a schematic view showing part of an XZ section of a lenssheet of a working example 3 in an enlarged scale;

FIG. 14 is a distribution diagram illustrating a light distributioncharacteristic of the lens sheet of the working example 3;

FIG. 15 is a schematic view showing part of an XZ section of a lenssheet of a working example 4 in an enlarged scale;

FIG. 16 is a distribution diagram illustrating a light distributioncharacteristic of the lens sheet of the working example 4;

FIG. 17 is a schematic view showing part of an XZ section of a lenssheet of a working example 5 in an enlarged scale;

FIG. 18 is a distribution diagram illustrating a light distributioncharacteristic of the lens sheet of the working example 5;

FIG. 19 is a schematic view showing part of an XZ section of a lenssheet of a working example 6 in an enlarged scale;

FIG. 20 is a distribution diagram illustrating a light distributioncharacteristic of the lens sheet of the working example 6;

FIG. 21 is a schematic view showing part of an XZ section of a lenssheet of a working example 7 in an enlarged scale;

FIG. 22 is a distribution diagram illustrating an orientationcharacteristic of the lens sheet of the working example 7;

FIG. 23 is a graph illustrating a peak luminance distribution whereK=−1;

FIG. 24 is a graph illustrating a peak luminance distribution whereK=−1.5;

FIG. 25 is a graph illustrating a peak luminance distribution whereK=−2;

FIG. 26 is a graph illustrating a peak luminance distribution whereK=−5;

FIG. 27 is a graph illustrating a peak luminance distribution whereK=−10;

FIG. 28 is a graph illustrating a peak luminance distribution whereK=−15;

FIG. 29 is a graph illustrating a peak luminance distribution whereK=−20;

FIG. 30 is a table illustrating a result of evaluation of lens sheets;

FIG. 31 is a table illustrating a result of evaluation of lens sheets;

FIG. 32 is a graph illustrating a relationship between the number ofconvex portions of a size equal to or greater than 0.2 μm and theluminance relative value;

FIG. 33 is a graph illustrating the number of convex portions of a sizeequal to or greater than 0.2 μm and the external appearance blurring;

FIG. 34 is a graph illustrating a relationship between the distancebetween convex portions of a size equal to or greater than 0.2 μm andthe luminance relative value;

FIG. 35 is a graph illustrating a relationship between the distancebetween convex portions of a size equal to or greater than 0.2 μm and aresult of a sliding test;

FIG. 36 is a graph illustrating a relationship between the distancebetween convex portions of a size equal to or greater than 0.2 μm andthe external appearance blurring;

FIG. 37 is a graph illustrating a relationship between the ten-pointaverage roughness SRz and the luminance relative value;

FIG. 38 is a graph illustrating a relationship between the ten-pointaverage roughness SRz and a result of a sliding test;

FIG. 39 is a graph illustrating a relationship between the height atwhich the convex portion area occupies 1% and the luminance relativevalue;

FIG. 40 is a graph illustrating the height at which the convex portionarea occupies 1% and a result of the sliding test;

FIG. 41 is a graph illustrating a relationship between the haze and theluminance relative value; and

FIG. 42 is a graph illustrating a relationship between the averageinclination gradient and the luminance relative value.

DETAILED DESCRIPTION

In the following, an embodiment of the present invention is describedwith reference to the drawings. It is to be noted that, in all of thefigures of the embodiment described below, like or correspondingelements are denoted by like reference characters.

Configuration of a Liquid Crystal Display Apparatus

FIG. 3 is a sectional view showing an example of a configuration of aliquid crystal display apparatus according to an embodiment of thepresent invention. Referring to FIG. 3, the liquid crystal displayapparatus includes a backlight 1 and a liquid crystal panel 2. While itis described here that the backlight 1 is of the direct type, thebacklight 1 may be of the edge light type (side light type).

The backlight 1 is for supplying light to the liquid crystal panel 2 andis disposed directly below the backlight 1. The liquid crystal panel 2is for temporally and spatially modulating the light supplied theretofrom the backlight 1 to display information. A pair of polarizing plates2 a and 2 b are provided on the opposite faces of the liquid crystalpanel 2. Each of the polarizing plate 2 a and the polarizing plate 2 btransmit one of orthogonally polarized light components of incidentlight therethrough and intercept the other one of the orthogonallypolarized light components by absorption. The polarizing plate 2 a andthe polarizing plate 2 b are provided such that, for example, thetransmission axes thereof are orthogonal to each other.

As seen in FIG. 3, the backlight 1 includes, for example, a reflectingplate 11, one or more light sources 12, a diffuser 13, a diffusing sheet17, a lens sheet 14, and a reflection type polarizer 18. The one orplural light sources 12 are for supplying light to the liquid crystalpanel 2 and are each in the form of, for example, a fluorescent lamp(FL), an EL (Electro Luminescence) element or an LED (Light EmittingDiode).

The reflecting plate 11 is provided such that it covers the one orplural light sources 12 from below and sidewardly and is for reflectinglight emitted downwardly or sidewardly from the one or plural lightsources 12 to direct the light toward the liquid crystal panel 2. It isto be noted that a chassis may be provided in place of the reflectingplate 11.

The diffuser 13 is provided above the one or plural light sources 12 andis for diffusing emitted light from the one or light sources 12 andreflected light from the reflecting plate 11 to make the luminanceuniform.

The diffusing sheet 17 is provided on the diffuser 13 and is for atleast diffusing the light diffused by the diffuser 17. Further, thediffusing sheet 17 may additionally have a function of condensing light.

The lens sheet 14 which is an example of an optical sheet is providedabove the diffuser 13 and is for enhancing the directivity and so forthof illumination light.

The reflection type polarizer 18 is provided on the lens sheet 14 and isfor transmitting one of orthogonally polarized light components of thelight whose directivity has been enhanced by the lens sheet 14 whilereflecting the other one of the orthogonally polarized light components.

In the following, a configuration of the lens sheet 14 described aboveis described in more detail.

Configuration of the Lens Sheet

FIG. 4 is a perspective view showing an example of a shape of the lenssheet 14 according to the embodiment of the present invention. Referringto FIG. 4, the lens sheet 14 has a form of a sheet and has, for example,a quadrangular shape as viewed from a principal face side thereof. Inthe present specification, a sheet includes not only a film-like sheetbut also sheets having various forms of thin plates having flexibilityor some degree of hardness.

In the following description, one principal face of the lens sheet 14 onthe side on which light from the light sources 12 is incident isreferred to as rear face, and the other principal face on the side fromwhich light from the light sources 12 is emitted is referred to as frontface.

A plurality of convex portions 16 are provided on the rear face side ofthe lens sheet 14, and a large number of cylindrical lens elements 15having a leftwardly and rightwardly symmetrical hyperboloidal face orparaboloidal face are juxtaposed in a direction perpendicular to thegenerating line of the hyperboloidal faces or paraboloidal faces on thefront face side of the lens sheet 14. The cylindrical lens elements 15have one focal distance fa on the side thereof from which light from thelight sources 12 is emitted. It is to be noted that, as shown in FIG. 4,an X axis is taken in parallel to the direction of the row of thecylindrical lens elements 15; a Y axis is taken in parallel to thedirection of the generating line of the cylindrical lens elements 15;and a Z axis is taken in parallel to the normal line direction to thelens sheet 14.

The width of the cylindrical lens elements 15 provided on the front faceside of the lens sheet 14, that is, a configuration unit width (pitch)D, is selected from within a range of 10 to 120 μm, and preferablyselected in accordance with pixels of the liquid crystal panel. Forexample, where the lens sheet 14 is used for a liquid crystal televisionset or a liquid crystal monitor for a personal computer, theconfiguration unit width (pitch) D is selected preferably within a rangeof 50 to 100 μm. On the other hand, where the lens sheet 14 is used fora monitor for a portable apparatus, the configuration unit width D ispreferably selected from within another range of 10 to 80 μm.

It is to be noted that the lens sheet 14 is provided between thediffuser 13 and the liquid crystal panel 2 such that the side thereof onwhich the plural cylindrical lens elements 15 are provided is opposed tothe liquid crystal panel 2.

Further, the shape of an XZ section of the cylindrical lens elements 15satisfies the following expression (1):Z=X ²/(R+√{square root over ( )}(R ²−(1+K)X ²))+AX ⁴ +BX ⁵ +CX ⁶+  (1)where R is the radius of curvature of a distal end vertex of thecylindrical lens elements 15, K is a conic constant, and A, B, C . . .are aspheric coefficients. It is to be noted that, in the presentspecification, “√{square root over ( )}” signifies a square root of avalue determined by a numerical expression following the same.

In the expression (1), the radius R of curvature of the distal endvertex, the conic constant K and the aspheric coefficients A, B, C, . .. are preferably set to values within numerical ranges of 0<R≦72,−15<K≦−1, R−K≧5, and 0≦A, B, C . . . <10⁻³ By defining the factorsmentioned within such numerical ranges as specified above, thedirectivity of the illumination light can be raised.

Further, where the configuration unit width D is D=50 μm, in theexpression (1), the radius R of curvature of the distal end vertex, theconic constant K and the aspheric coefficients A, B, C, . . . arepreferably set to values within numerical ranges of 0<R≦+, −15<K≦−1,R−K≧5, and 0≦A, B, C . . . <10⁻³. By defining the factors mentionedwithin such numerical ranges as specified above, the directivity of theillumination light can be raised.

Further, in the expression (1), the radius R of curvature of the distalend vertex, the conic constant K and the aspheric coefficients A, B, C,are preferably set to values within numerical ranges of R≧0, K<−1,0<A<10⁻³, and 0≦B, C . . . <10⁻³. By defining the factors mentionedwithin such numerical ranges as specified above, the directivity of theillumination light and the angular of view can be raised.

Where the configuration unit width D is D=20 μm, the radius R ofcurvature of the distal end vertex and the conic constant K arepreferably set to values within numerical ranges of 0<R≦12 μm, −15<K≦−1,R−K ≧5, and 0<A, B, C . . . <10⁻³.

Where the configuration unit width D is D=80 μm, the radius R ofcurvature of the distal end vertex and the conic constant K arepreferably set to values within numerical ranges of 0<R≦48 μm, −15<K≦−1,R−K ≧5, and 0<A, B, C . . . <10⁻³.

The height of the convex portions 16 provided on the rear face of thelens sheet 14 is preferably set equal to or more than 0.20 μm from anaverage center plane (JIS B0601-1994). Further, the density of theconvex portions 16 having a height of 0.20 μm or more from the averagecenter plane is preferably set to a value equal to or higher than 70/mm²but equal to or lower than 500/mm². Further, the average distance of theconvex portions 16 having a height of 0.20 μm or more from the averagecenter plane is preferably set to a value within a region equal to orhigher than 50 μm but equal to or lower than 120 μm.

Further, the convex portions 16 provided on the rear face of the lenssheet 14 are preferably provided such that, in a state wherein thecylindrical lens elements 15 are not formed, the degree of cloudiness ofthe lens sheet 14 is equal to or lower than 60%, and more preferablyprovided such that the degree of cloudiness of the lens sheet 14 isequal to or lower than 20%.

Furthermore, the convex portions 16 provided on the rear face of thelens sheet 14 are preferably provided such that the ten-point averageroughness SRz is set to a value within a range equal to or higher than 1μm but equal to or lower than 15 μm. Further, the convex portions 16 onthe one principal face side of the lens sheet 14 are preferably providedsuch that the height thereof at which the convex portion area occupies1% is set to a value equal to or greater than 1 μm but equal to orsmaller than 7 μm.

Now, a method of producing the lens sheet according to the embodiment ofthe present invention is described.

First, an extruded sheet precision molding apparatus for use with theproduction method for the lens sheet according to the embodiment of thepresent invention is described with reference to FIG. 5.

Configuration of the Extruded Sheet Precision Molding Apparatus

Referring to FIG. 5, the extruded sheet precision molding apparatusincludes an extruder 21, a T die 22, a forming roll 23, an elastic roll24 and a cooling roll 25.

For molding of the lens sheet 14, at least one kind of transparentthermoplastic resin is used. As the thermoplastic material, athermoplastic material having a refractive index of 1.4 or more ispreferably used taking a function of controlling the light emittingdirection into consideration. As such resins, for example, apolycarbonate resin, an acrylic resin represented by a polymethylmethacrylate resin, a polyester resin or an amorphous copolymerpolyester resin represented by polyethylene terephthalate, a polystyreneresin, a polyvinylchloride resin and so forth can be listed.

Further, where the transfer performance of a lens pattern by a meltextrusion method is taken into consideration, more preferably the meltviscosity around a molding temperature is equal to or higher than 1,000Pa but equal to or lower than 10,000 Pa.

Furthermore, at least one kind of release agent is preferably containedin the thermoplastic resin. Where a release agent is contained in thismanner, the close contact property between the forming roll 23 and asheet when the sheet is to be exfoliated from the forming roll 23 can beadjusted to prevent an exfoliation line from being formed on the lenssheet 14.

The amount of the release agent to be added to the thermoplasticmaterial is preferably equal to or more than 0.02 wt % but equal to orsmaller than 0.4 wt %. If the amount decreases further than 0.02 wt %,then the releasability is deteriorated and an exfoliation line is formedon the lens sheet 14. On the other hand, where the amount increasesfurther than 0.04 wt %, then the releasability becomes excessively high.Consequently, before the transparent thermoplastic resin cures, it isexfoliated from the forming roll 23, resulting in a failure that theshape of the cylindrical lens elements 15 is deformed.

Further, at least one kind of ultraviolet absorbing agent or lightstabilizer is contained in the thermoplastic resin. Where theultraviolet absorbing agent or light stabilizer is contained in thismanner, a color change of the thermoplastic resin by light irradiationfrom a light source can be suppressed.

The amount of the ultraviolet absorbing agent or light stabilizer to beadded to the thermoplastic resin is preferably equal to or greater than0.02 wt % but equal to or lower than 0.4 wt %. Where the amountdecreases further than 0.02 wt %, it becomes impossible to suppress ahue change. On the other hand, where the amount increases further than0.4 wt %, the lens sheet 14 becomes yellowish.

As the ultraviolet absorbing agent, ultraviolet absorbing agents of thesalicylic acid type, benzophenone type, benzotriazole type,cyanoacrylate type and so forth can be listed. More particularly, forexample, Adekastab LA-31, Adekastab LA-32 (by ADEKA Corporation),Cyasorb UV-5411 (by Sun Chemical Company Ltd.), Tinuvin P, Tinuvin 234,Tinuvin 320, Tinuvin 327 (by Nihon CibaGeigy K. K.), Sumisorb 110,Sumisorb 140 (by Sumitomo Chemical Co., Ltd.), Kemisorb 110, Kemisorb140, Kemisorb 12, Kemisorb 13 (by Chemipro Kasei Kaisha, Ltd.), UvinulX-19, Uvinul Ms-40 (by BASF), Tomisorb 100, Tobisorb 600 (by YoshitomiPharmaceutical Industries, Ltd.), Viosorb-90 (by Kyodo Chemical Co.,Ltd.) and so forth are listed. Meanwhile, as the light stabilizer, ahindered amine light stabilizer and so forth are listed, and moreparticularly, for example, Adekastab LA-52 (by ADEKA Corporation), SanolLS-770, Sanol LS-765, Sanol Ls774 (by Sankyo Co., Ltd.), Sumisorb TM-061(by Sumitomo Chemical Co., Ltd.) and so forth are listed.

Further, also it is possible to add, in addition to the release agentand the ultraviolet absorbing agent described above, such an additive asan anti-oxidizing agent, an antistatic agent, a coloring agent, aplasticizer, a compatibilizer, a fire retardant or the like. However,most additives make a factor of generation of gas upon heating in meltextrusion of the T die 22 or the like and give rise to deterioration ofthe film formation or of the working environment. Therefore, the totalamount of additives is preferably minimized, and the amount of additivesto be added to a thermoplastic resin is preferably set equal to orsmaller than 2 wt %.

The extruder 21 melts a resin material supplied thereto from a hoppernot shown and supplies the molten resin material to the T die 22. The Tdie 22 has a “-” shaped opening, and expands the resin material suppliedthereto from the extruder 21 so as to have a width of a sheet to bemolded and discharges the expanded resin material.

The forming roll 23 has a cylindrical shape and is configured to bedriven to rotate around an axis of rotation which is a center axisthereof. Further, the forming roll 23 is configured so as to be cooled.In particular, the forming roll 23 has one, two or more flow paths forcirculation of a coolant in the inside thereof. As the coolant, forexample, an oil medium is used, and the temperature of this oil mediumis varied within a range, for example, from 120° C. to 230° C.

A sculpture shape for transferring a fine pattern to a sheet dischargedfrom the T die 22 is provided on a cylindrical surface of the formingroll 23. The sculpture shape is a fine concave and convex shape fortransferring, for example, the cylindrical lens elements 15 to a sheet.The concave and convex shape is formed, for example, by precisioncutting by means of a diamond cutting tool. Further, the sculpture shapeis formed toward a circumferential direction or a widthwise direction(heightwise direction) of the forming roll 23 having a cylindricalshape.

The elastic roll 24 has a cylindrical shape and is configured to bedriven to rotate around an axis of rotation which is the center axisthereof. Further, the surface of the elastic roll 24 is formed forelastic deformation such that, when a sheet is nipped by the formingroll 23 and the elastic roll 24, a face of the elastic roll 24contacting with the forming roll 23 is elastically deformed into asquashed state.

The elastic roll 24 is covered with a seamless tube formed from, forexample, plated Ni, and a resilient member for allowing the surface ofthe elastic roll 24 to be elastically deformable is provided in theinside of the elastic roll 24. The configuration and the material of theelastic roll 24 are not limited particularly only if the surface of theelastic roll 24 elastically deforms when it contacts with the formingroll 23 with a predetermined pressure. For example, a rubber material, ametal material or a composite material may be used as the material. Theelastic roll 24 is not limited to a roll-shaped one, but a belt-shapedone may be used.

When the convex portions 16 are to be provided on the rear face of thelens sheet 14, recesses for forming the convex portions 16 on the rearface side of the lens sheet 14 are provided on the cylindrical face ofthe elastic roll 24. The elastic roll 24 is configured so as to becooled. In particular, the elastic roll 24 has one, two or more flowpaths for circulation of a coolant in the inside thereof. As thecoolant, for example, water can be used. Then, a temperature regulatorof the pressurized hot water type not shown is used to set the basictemperature, for example, to 80° C. and 130° C. It is to be noted thatan oil temperature regulator may be used as the temperature regulator.

The cooling roll 25 has a cylindrical shape and is configured to bedriven to rotate around an axis of rotation which is the center axisthereof. The cooling roll 25 is configured so as to be cooled. Inparticular, the cooling roll 25 has one, two or more flow paths forcirculation of a coolant in the inside thereof. As the coolant, forexample, water can be used. Then, a temperature regulator of thepressurized hot water type not shown is used to set the basictemperature, for example, to 115° C. It is to be noted that an oiltemperature regulator may be used as the temperature regulator.

Production Method for the Lens Sheet

A production method for a lens sheet according to the embodiment of thepresent invention is described below.

First, a resin material is melted by the extruder 21 and successivelysupplied to the T die 22 so that a sheet is discharged continuously fromthe T die 22.

Then, the sheet discharged from the T die 22 is nipped by the formingroll 23 and the elastic roll 24. Consequently, the sculpture shape ofthe forming roll 23 is transferred to the front face of the sheet whilethe concave and convex shape of the elastic roll 24 is transferred tothe rear face of the sheet. Thereupon, the surface temperature of theforming roll 23 is kept within a temperature range from Tg+20° C. toTg+45° C., and the surface temperature of the elastic roll 24 is keptwithin another temperature range from 20° C. to Tg° C. Here, Tg is aglass transition temperature of the resin material. Since the surfacetemperatures of the forming roll 23 and the elastic roll 24 are keptwithin the temperature ranges specified as above, the sculpture shapecan be transferred well to the sheet. Further, the temperature of theresin material when the sculpture shape is transferred to the sheet ispreferably set to Tg+50° C. to Tg+230° C. and more preferably set toTg+80° C. to Tg+200° C. Where the temperature of the resin is keptwithin the temperature range specified above, the sculpture shape can betransferred well to the sheet.

Then, while the sheet is nipped by the forming roll 23 and the coolingroll 25 to suppress fluttering thereof, the sheet is exfoliated from theforming roll 23 by the cooling roll 25. Thereupon, the surfacetemperature of the cooling roll 25 is kept within a temperature rangeequal to or lower than Tg. Where the surface temperature of the coolingroll 25 is kept within such a temperature range as specified above andthe sheet is nipped by the forming roll 23 and the cooling roll 25 tosuppress fluttering thereof, the sheet can be exfoliated well from theforming roll 23. Further, the temperature of the resin material uponexfoliation is preferably equal to or higher than Tg, and morepreferably is Tg+20° C. to Tg+85° C. and still more preferably is Tg+30°C. to Tg+60° C. Where the temperature of the resin is kept within such atemperature range as specified just above and the sheet is nipped by theforming roll 23 and the cooling roll 25 to suppress fluttering thereof,the sheet can be exfoliated well from the forming roll 23. According tothe foregoing, an object lens sheet can be obtained.

According to the embodiment of the present invention, the followingeffects can be achieved.

In a conventional production method for a lens sheet, a lens shape isformed principally with a UV (ultraviolet rays) curing resin (forexample, a UV curing acrylic resin or the like) on a film substrate ofpolyethylene terephthalate (PET) or the like. This production method hasproblems that the UV curing resin is expensive and that, since it isnecessary to perform UV irradiation sufficiently on the UV curing resinin order to harden the resin, the production speed is low. Further, theproduction method has a problem also that, since a two-layer structureof a sheet and a lens layer is used, warping is liable to occur due tothe difference in expansion coefficient by the heat or temperature andthe assembly process is complicated.

Against the problems, the lens sheet production method according to thepresent embodiment can achieve, because it uses an integrated moldedarticle by thermal transfer to a thermoplastic resin, such specialeffects that a less expensive material can be used, that theproductivity of a lens sheet can be enhanced and that also appearance ofwarping on a lens sheet can be suppressed.

In the following, the present invention is described in connection withworking examples. However, the present invention is not limited only tothe working examples.

The inventor of the present invention performed a study through asimulation in which the numerical values of the radius R of curvature,the conic constant K and the aspheric coefficients A, B, C . . . in theexpression (1) given hereinabove were varied in order to define theradius R of curvature, the conic constant K and the asphericcoefficients A, B, C . . . .

CONVENTIONAL EXAMPLE

FIG. 6 shows part of an XZ section of a prism sheet of a conventionalexample in an enlarged scale. A plurality of very small prisms areprovided successively on the surface of the prism sheet. It is to benoted that, in FIG. 6, a point A indicates a vertex of a prism, andanother point B and a further point C indicate each a joining point withan adjacent prism, and a still further point O is an imaginary lightstart point just below the vertex A. A yet further point P indicates animaginary light start point just below the joining point B. Further, inthe following description, a face between the vertex A and the joiningpoint B is referred to as AB face, and a face between the vertex A andthe joining point C is referred to as AC face.

Further, FIG. 6 shows a locus of a light flux Ω which enters the AB facefrom the imaginary light start point O and a locus of another light fluxΨ which enters the AB face and the AC face from the imaginary lightstart point P. The loci of the light flux Ω and the light flux Ψ weredetermined through a simulation. It is to be noted that, also in theworking examples hereinafter described, like or corresponding elementsare denoted by like reference characters.

FIG. 7 illustrates a luminous intensity distribution characteristic ofthe prism sheet of the conventional example. FIG. 8 illustrates a visualfield characteristic of the prism sheet of the conventional example. Itis to be noted that, in FIGS. 7 and 8, a distribution surrounded by aframework t1 corresponds to the first order transmission light, and adistribution surrounded by another framework t2 corresponds to thesecond order transmission light. The distribution diagram of FIG. 7shows circles whose center is set to 0° C. and indicate angles such thatthe first circle from the center indicates an angle of 10°, the secondcircuit indicates another angle of 20°, . . . , and the outermost circleindicates 90°. Further, the distribution diagrams of FIGS. 7 and 8 aredrawn through a computer simulation. Also the distribution diagrams ofthe working examples hereinafter described depend upon a simulationsimilarly.

From FIG. 7, it can be confirmed in what angle light emitted from theprism sheet expands. Further, it can be seen that a distributioncorresponding to the second order transmission light T2 appears in theproximity of 70° above and below the center. Further, from FIG. 8, itcan be seen that the angular field of view by the half value width withrespect to the front face luminance is approximately 100°.

Then, a prism of a triangular shape described hereinabove was producedon the one principal face of the sheet by a melt extrusion method, andthe shape of the prism was evaluated.

In the following, a production method for a lens sheet by the meltextrusion method is described particularly.

First, the elastic roll was produced in the following manner. A seamlesstube was formed by Ni plating, and a Cr plating process was performedfor the surface of the seamless tube. Thereafter, the plated Cr layerwas polished to 0.2 S to produce a seamless tube (hereinafter referredto as flexible sleeve) having a thickness of 340 microns.

Then, a resilient member was adhered to a roll in which coolant can becirculated, and the flexible sleeve was fitted on the resilient memberto obtain an elastic roll having a configuration that cooling water canbe circulated between the resilient member and the flexible sleeve. Itis to be noted that the resilient member was made of nitrile-butadienerubber (NBR) having a hardness of 85 degrees with a thickness of 20 mm.Further, the diameter Φ of the elastic roll was set to 260 mm, and theface length (width of the forming roll) was set to 450 mm.

Thereafter, a forming roll having a structure wherein coolant can becirculated in the inside thereof through a plurality of flow paths sothat the temperature distribution can be reduced was prepared. It is tobe noted that the material was S45C and was subject to hardening andtempering and then to mirror finish (equal to or less than 0.5 S) and anelectroless NiP (Nickel and Phosphorus) plating (100 microns thick)process.

A sculpture shape was formed on the cylindrical face of the forming rollin the following manner. First, a diamond cutting tool having apredetermined shape was set in position on a superfine lathe wherein theforming roll was placed in a chamber of a constant temperature and aconstant humidity (temperature 23° C., humidity 50%). Then, lenspatterns of the prism of the triangular shape described above wereformed in a circumferential direction of the forming roll. It is to benoted that the forming roll has a diameter of Φ0300, a face length of460 mm and a groove working width of 300 mm.

An oil medium was used as the coolant for the forming roll. Water wasused as the coolant for the elastic roll and the cooling roll, and atemperature regulator of the pressurized hot water type was used toregulate the temperature of the coolants.

As the extruder, an extruder including a screw with a vent having adiameter of Φ50 mm and having no gear pump was used. Further, as the Tdie, a coach hanger type die was used, and the lip width of the same was550 mm and the lip gap was 1.5 mm. Further, the air gap was 105 mm.

The extruded sheet precision molding apparatus having the configurationdescribed above was used to perform molding of a lens sheet.

First, the polycarbonate E2000R (by Mitsubishi Engineering-PlasticCorporation) was extruded from the T die. Then, the material was nippedby the forming roll and the elastic roll and then wrapped around theforming roll. It is to be noted that the surface temperature of theforming roll was kept at Tg+35° C., and the surface temperature of theelastic roll was kept at 75° C. Here, Tg is the glass transitiontemperature of the polycarbonate resin.

Thereafter, the sheet was exfoliated from the forming roll by thecooling roll. It is to be noted that the surface temperature of thecooling roll was kept at 115° C. Further, the speed of a takeupapparatus was 7 m/min. As a result of the foregoing, a lens sheet of athickness of 220 microns having grooves transferred to one of theprincipal faces thereof was obtained.

The surface temperatures of the forming roll and the elastic rolldescribed above were obtained such that a sensor was contacted with theroll surfaces to perform measurement at a position immediately precedingto the nit point at which the measurement is least likely to beinfluenced by the heat of the resin. Meanwhile, the surface temperatureof the cooling roll was obtained such that a sensor was contacted withthe surface of the cooling roll to perform measurement at a position atwhich the film is nipped by the cooling roll and the forming roll. It isto be noted that, as the thermometers, a handy type digital thermometer(by Chino, commodity name: ND511-KHN) was used, and as the sensors, asensor for surface temperature measurement (by Anritsu Meter Co., Ltd.,commodity name U-161K-00-D0-1) was used.

Thereafter, the prism lens formed on one of the principal surfaces ofthe prism sheet in such a manner as described above and the prism lensdescribed hereinabove with reference to FIG. 6 were compared with eachother in shape. As a result, it was found that a desired lens shape wasnot successfully obtained because it was impossible to cause thethermoplastic resin to advance into a vertex portion of the lens patternof the prism of the triangular shape.

WORKING EXAMPLE 1

(Where R=3, K=−2, A=10⁻⁵, B, C . . . =0)

FIG. 9 shows part of an XZ section of a lens sheet of a working example1 in an enlarged scale. A large number of cylindrical lens elementshaving a finite focal distance on the emission side of illuminationlight and having a leftwardly and rightwardly symmetrical, high-orderaspheric face are arrayed successively on the lens sheet. The asphericsectional shape is represented by Z=X²/(3+√{square root over ()}(9+X²))+10⁻⁵X⁴ which satisfies the expression (1).

In the following, action and effects of the lens sheet of the workingexample 1 with respect to a light flux Ω incident from a perpendiculardirection and another light flux Ψ incident from a sideward directionare described with reference to FIG. 9.

Light Flux Ω Incident from a Perpendicular Direction

First, action and effects of the lens sheet with respect to a light fluxΩ incident from a perpendicular direction are described. As seen in FIG.9, since a large number of cylindrical lens elements having a high-orderaspheric face are arrayed successively, the light flux Ω can berefracted and transmitted forwardly of the lens sheet, and thiscontributes to enhancement of the luminance in the front face directionwhen compared with the conventional prism sheet.

Light Flux Ψ Incident from a Sideward Direction

Now, action and effects of the lens sheet with respect to a light flux Ψincident from a sideward direction are described. As seen in FIG. 9, alight flux Ψ emitted from an imaginary light start point P just below ajoining point B between aspheric faces and entering the AB face istotally reflected most by the AB face and is refracted or totallyreflected by the AC face to form a return light component R. Therefore,the probability that the light flux Ψ may contribute to generation ofside lobe light as a second-order transmission light component T2 can bereduced, and the light flux Ψ can contribute to enhancement of theluminance in the front face direction.

Furthermore, also on the face in the proximity of the vertex A on theside between the points A and C, the angle of a normal line to the faceforms a shallow angle with respect to the Z axis with regard to areflected light flux from the first totally reflecting face (AB face).Therefore, an effect that the reflected light flux is totally reflectedto form the return light component R is exhibited.

Furthermore, part of the light flux Ψ incident to the AC face isdistributed forwardly by a refraction effect provided by the curved faceshape of the AC face.

Furthermore, also on the curved face in the proximity of the vertex, thereflected light flux from the AB face undergoes a refractiontransmission effect higher than that of the conventional prism shape andundergoes even a total reflection effect.

FIG. 10 illustrates a light distribution characteristic of the lenssheet of the working example 1. As seen in FIG. 10, with the lens sheetof the working example 1, the second-order transmission light componentT2 is reduced when compared with the prism sheet of the conventionalexample described hereinabove.

In this manner, in the lens sheet of the working example 1, by improvingthe refraction and transmission effect to the front face side over anoverall area from a perpendicular component direction describedhereinabove and the refraction capacity and the total reflectioncapacity for an incident light flux from a side face direction, thefirst order transmission light can be increased thereby to raise thefront face luminance while the light distribution is maintained in theforward direction. Further, by suppressing the second order transmissionlight component T2 to increase the contribution to the return lightcomponent R, the light can be utilized effectively, and therefore, thegain characteristic of light can be enhanced.

Then, the toroidal lens elements formed on one of the principal faces ofthe lens sheet in such a manner as described above and the toroidal lenselement represented by Z=X²/(3+√{square root over ( )}(9+X²))+10⁻⁵X⁴specified as above were compared in shape with each other. As a result,it was found that the two have a substantially same shape. In otherwords, it was found that the thermoplastic resin can be advanced into avertex portion of the lens pattern of each toroidal lens element and adesired toroidal lens shape can be obtained.

WORKING EXAMPLE 2

(Where R=5, K=−10, A=5×10⁻⁵, B, C . . . =0)

FIG. 11 shows part of an XZ section of a lens sheet of a working example2 in an enlarged scale. Cylindrical lens elements having a finite focaldistance on the emission side of illumination light and having aleftwardly and rightwardly symmetrical, high-order aspheric face arearrayed successively on the lens sheet. This aspheric face isrepresented by Z=X²/(5+√{square root over ( )}(25+9X²))+5×10⁻⁵X⁴ whichsatisfies the expression (1).

In the following, action and effects of the lens sheet of the workingexample 2 with respect to a light flux Ω incident from a perpendiculardirection and another light flux Ψ incident from a sideward directionare described with reference to FIG. 11.

As seen in FIG. 11, the sectional shape exhibits a curved face of agreat curvature when compared with that of the sectional shape of thelens sheet of FIG. 9, and although the expansion of the refractedtransmitted light of the light flux Ω is subject to a variation, therefracted transmitted light is distributed forwardly. Further, since thetotal reflection effect of the AB face and the AC face increases, thesecond order transmission light component T2 can be reduced. As regardsthe transmission direction through the AC face, the variation of thenormal line direction increases and the incidence angle of the incidentlight flux becomes shallow. Therefore, although the refraction effectdecreases, the forward light distribution is not deteriorated.

FIG. 12 illustrates a light distribution characteristic of the lenssheet of the working example 2. As shown in FIG. 12, with the lens sheetof the working example 2, the second order transmission light componentT2 is reduced when compared with the conventional prism sheet describedhereinabove.

Then, a lens sheet was produced in a similar manner as in the workingexample 1 described hereinabove, and the toroidal lens elements formedon one of the principal faces of the lens sheet and the toroidal lenselement represented by Z=X²/(5+√{square root over ( )}(25+9X²))+5×10⁻⁵X⁴specified as above were compared in shape with each other. As a result,it was found that the two have a substantially same shape.

WORKING EXAMPLE 3

(Where R=1, K=−2, A=10⁻⁵, B, C . . . =0)

FIG. 13 shows part of an XZ section of a lens sheet of a working example3 in an enlarged scale. Cylindrical lens elements having a finite focaldistance on the emission side of illumination light and having aleftwardly and rightwardly symmetrical, high-order aspheric face arearrayed successively on the lens sheet. This aspheric face shape isrepresented by Z=X²/(1+√{square root over ( )}(1+X²))+10⁻⁵X⁴ whichsatisfies the expression (1).

In the following, action and effects of the lens sheet of the workingexample 3 with respect to a light flux Ω incident from a perpendiculardirection and another light flux Ψ incident from a sideward directionare described with reference to FIG. 13.

As seen in FIG. 13, part of a light flux Ω emitted from an imaginarylight start point O is totally reflected by the face in the proximity ofa point A and can auxiliary enhance the front face luminance as a returnlight component R. Further, the efficiency in which a light flux Ψemitted from another imaginary light start point P can be utilized as areturn light component R by the total reflection and a refractioncapacity for the light flux Ψ is raised to moderate appearance of thesecond-order transmission light component T2.

FIG. 14 is a distribution diagram representing the light distributioncharacteristic of the lens sheet of the working example 3. As shown inFIG. 14, with the lens sheet of the working example 3, the second ordertransmission light component T2 is reduced when compared with the prismsheet of the conventional example described hereinabove.

Then, a lens sheet was produced in a similar manner as in the workingexample 1, and the toroidal lens elements formed on one of the principalfaces of the lens sheet and the toroidal lens element represented byZ=X²/(1+√{square root over ( )}(1+X²))+10⁻⁵X⁴ specified as above werecompared in shape with each other. As a result, it was found that thetwo have a substantially same shape.

WORKING EXAMPLE 4

(Where R=1, K=−2, A=10⁻⁵, B=0, C=2×10⁻⁵, D, E . . . =0)

FIG. 15 shows part of an XZ section of a lens sheet of a working example4 in an enlarged scale. Cylindrical lens elements having a finite focaldistance on the emission side of illumination light and having aleftwardly and rightwardly symmetrical, high-order aspheric face arearrayed successively on the lens sheet. This aspheric face isrepresented by Z=X²/(1+√{square root over ( )}(1+X²))+10⁻⁵X⁴+2×10⁻⁵X⁶which satisfies the expression (1).

In the following, action and effects of the lens sheet of the workingexample 4 with respect to a light flux Ω incident from a perpendiculardirection and another light flux Ψ incident from a sideward directionare described with reference to FIG. 15.

As seen in FIG. 15, part of a light flux Ω emitted from an imaginarylight start point O is totally reflected by the face in the proximity ofa point A and can auxiliary enhance the front face luminance as a returnlight component R. Further, the efficiency in which a light flux Ψemitted from another imaginary light start point P can be utilized as areturn light component R by the total reflection and a refractioncapacity for the light flux Ψ is raised to moderate appearance of thesecond-order transmission light component T2.

FIG. 16 illustrates a light distribution characteristic of the lenssheet of the working example 4. As shown in FIG. 16, with the lens sheetof the working example 4, the second order transmission light componentT2 is reduced when compared with the prism sheet of the conventionalexample described hereinabove.

Then, a lens sheet was produced in a similar manner as in the workingexample 1, and the toroidal lens elements formed on one of the principalfaces of the lens sheet and the toroidal lens element represented byZ=X²/(1+√{square root over ( )}(1+X²))+10⁻⁵X⁴+2×10⁻⁵X⁶ specified asabove were compared in shape with each other. As a result, it was foundthat the two have a substantially same shape.

WORKING EXAMPLE 5

(Where R=25, K=−2, A=5×10⁻⁵, B, C . . . =0)

FIG. 17 shows part of an XZ section of a lens sheet of a working example5 in an enlarged scale. FIG. 20 illustrates a visual fieldcharacteristic of the lens sheet of the working example 5. A crosssection of cylindrical lens elements provided on a face of the lenssheet on the side from which light is emitted has an aspheric facesectional shape having a finite focal distance on the emission side ofillumination light as seen in FIG. 17. The sectional shape isrepresented by the following expression which is obtained bysubstituting R=25, K=−2, A=5×10⁻⁵, B, C . . . =0 into the expression(1):Z=X ²/(25+√{square root over ( )}(625+10X ²))+5×10⁻⁵ X ⁴

In the following, action and effects of the lens sheet of the workingexample 5 with respect to a light flux Ω incident from a perpendiculardirection and another light flux Ψ incident from a sideward directionare described with reference to FIG. 17.

Light Flux Ω Incident from a Perpendicular Direction

First, action and effects of the lens sheet with respect to the lightflux Ω incident from a perpendicular direction are described. In thelens sheet of the working example 5, the incident light flux Ω is allrefracted and transmitted forwardly of the lens sheet. Consequently, aneffect that the distribution light ratio to the sheet front facedirection can be increased can be achieved. In particular, in the lenssheet of the working example 5, since the first-order transmission lightcan all be refracted and transmitted forwardly due to the aspheric faceshape provided on one of the principal faces, an effect that thecharacteristic of the first order transmission light can be improved canbe achieved.

In contrast, in the prism sheet of the conventional example describedhereinabove, since part of the light flux Ω which is incident upon aportion in the proximity of a vertex from within the light flux Ω has anincident angle exceeding the critical angle θc=sin⁻¹(1/n), it is totallyreflected to form return light. For example, where the sheet material ispolycarbonate (n=1.59), the light flux Ω having an incident angleexceeding the critical angle θc=38.97° is totally reflected to formreturn light. It is to be noted that part of the return light isre-introduced into the prism sheet by a diffuser or the like and thenutilized effectively.

Light Flux Ψ Incident from a Sideward Direction

Now, action and effects of the lens sheet with respect to the light fluxΨ incident from a sideward direction are described. Part of the lightflux Ψ is totally reflected by the AB face and is refracted or totallyreflected by the AC face so that the probability that the totallyreflected light flux Ψ may contribute to generation of side lobe lightas second order transmission light is reduced. Meanwhile, the other partof the light flux Ψ incident on the AB face is refracted and transmittedso that it may form transmission light which expands the angular fieldof view without having an influence on side robe light.

Here, paying attention to a portion of the AC face in the proximity ofthe vertex, in the lens sheet of the working example 5, a normal line tothe AC face in the proximity of the vertex forms a shallow angle withrespect to the Z axis. Accordingly, an effect that the reflected lightflux Ψ from the AC face can be totally reflected by the portion of theAC face in the proximity of the vertex to form the return light can beachieved. In particular, in the prism sheet of the conventional example,the light flux Ψ incident on a portion of the AC face in the proximityof the vertex A from within the light flux Ψ coming to the AC face afterreflected by the AB face forms side robe light. However, in the lenssheet of the working example 5, the light flux Ψ incident on the AC facein the proximity of the vertex A from within the light flux Ψ coming tothe AC face after reflected by the AB face can be totally reflected toform return light.

Further, from within the light flux Ψ incident on the AC face from theimaginary start point P, the light flux Ψ in a region up to a portion ofthe AC face in the proximity of the joining point C is distributedforwardly by a refraction effect of the curved face. Therefore, anexpansion effect of the angular field of view can be anticipated.Further, the light flux Ψ in the proximity of the joining point C whichis a light flux to a sideward direction which can originally become siderobe light is refracted and transmitted by the AC face and re-enters anadjacent aspheric face side to form return light. Therefore, an effectthat side robe light can be suppressed can be anticipated.

As described above, an overall forward refraction transmission effect ofthe incidence light flux Ω from a perpendicular direction, a refractioncapacity and a total reflection capacity for the incident light flux Ψfrom a sideward direction and a return light effect of side facedistribution light can be enhanced.

Consequently, the first order transmission light can be increased toraise the front face luminance while the light distribution ismaintained in the forward direction. Further, the second ordertransmission light can be suppressed to give rise to an expansion effectof the angular field of view. Furthermore, the contribution to returnlight can be increased to implement effective utilization of light(refer to FIG. 18).

Then, a lens sheet was produced in a similar manner as in the workingexample 1 described hereinabove, and the toroidal lens elements formedon one of the principal faces of the lens sheet and the toroidal lenselement represented by Z=X²/(25+√{square root over ()}(625+10X²))+5×10⁻⁵X⁴ specified as above were compared in shape witheach other. As a result, it was found that the two have a substantiallysame shape.

WORKING EXAMPLE 6

(Where R=10, K=−41, A=6×10⁻⁵, B, C . . . =0)

FIG. 19 shows part of an XZ section of a lens sheet of a working example6 in an enlarged scale. FIG. 20 illustrates a visual fieldcharacteristic of the lens sheet of the working example 6. A crosssection of cylindrical lens elements provided on a face of the lenssheet on the side from which light is emitted has an aspheric facesectional shape having a finite focal distance as seen in FIG. 19. Thesectional shape is represented by the following expression which isobtained by substituting R=10, K=−41, A=6×10⁻⁵, B, C . . . =0 into theexpression (1):Z=X ²/(10+√{square root over ( )}(100+40X ²))+6×10⁻⁵ X ⁴

From FIGS. 19 and 20, it can be seen that the lens sheet of the workingexample 6 can achieve action and effects similar to those of the lenssheet of the working example 5 described hereinabove with respect to thelight flux Ω incident from a perpendicular direction and the light fluxΨ incident from a sideward direction.

Then, a lens sheet was produced in a similar manner as in the workingexample 1 described hereinabove, and the toroidal lens elements formedon one of the principal faces of the lens sheet and the toroidal lenselement represented by Z=X²/(10+√{square root over ()}(100+40X²))+6×10⁻⁵X⁴ specified as above were compared in shape witheach other. As a result, it was found that the two have a substantiallysame shape.

WORKING EXAMPLE 7

(Where R=40, K=−201, A=6×10⁻⁵, B, C . . . =0)

FIG. 21 shows part of an XZ section of a lens sheet of a working example7 in an enlarged scale. FIG. 22 illustrates a orientation characteristicof the lens sheet of the working example 7. A cross section ofcylindrical lens elements provided on a face of the lens sheet on theside from which light is emitted has an aspheric face sectional shapehaving a finite focal distance as seen in FIG. 21. The sectional shapeis represented by the following expression which is obtained bysubstituting R=40, K=−201, A=6×10⁻⁵, B, C . . . =0 into the expression(1):Z=X ²/(40+√{square root over ( )}(1600+200X ²))+6×10⁻⁵ X ⁴

From FIGS. 21 and 22, it can be seen that the lens sheet of the workingexample 6 can achieve action and effects similar to those of the lenssheet of the working example 5 described hereinabove with respect to thelight flux Ω incident from a perpendicular direction and the light fluxΨ incident from a sideward direction.

Then, a lens sheet was produced in a similar manner as in the workingexample 1 described hereinabove, and the toroidal lens elements formedon one of the principal faces of the lens sheet and the toroidal lenselement represented by Z=X²/(40+√{square root over ()}(1600+200X²))+6×10⁻⁵X⁴ specified as above were compared in shape witheach other. As a result, it was found that the two have a substantiallysame shape.

Further, as shown in FIGS. 8, 18, 20 and 22, the angular field of viewaccording to a half value width with respect to the front face luminanceexhibits the following values in the conventional example and theworking examples 5 to 7:

Conventional example: 100°

Working example 5: 145°

Working example 6: 145°

Working example 7: 150°

Accordingly, while the conventional prism sheet has a problem that theangular field of view is approximately 100° and is narrow, the lenssheets of the working examples 5 to 7 have an advantage that the angularfield of view is approximately 150° and is wide. In other words, thelens sheets of the working examples 5 to 7 can achieve a superior effectthat the angular field of view can be enhanced significantly whencompared with the conventional prism sheet.

It can be recognized that, from the working examples 1 to 4 describedabove, the following effects can be achieved by applying the conditionsof 0<R≦30, R−K≧5, −15<K≦−1, 0<A, B, C . . . <10⁻³ to the expression (1).In particular, it can be recognized (1) that the highest luminance canbe obtained in the front face direction, (2) that a high luminancedistribution can be implemented in a direction within a predeterminedangular field of view, (3) that the second order transmission light canbe suppressed.

Further, it can be recognized that, from the working examples 5 to 7described above, the following effects can be achieved by applying theconditions of 0≧R, K<−1, 0<A<10⁻³, 0≦B, C . . . <10⁻³ to the expression(1). In particular, it can be recognized (1) that the highest luminancecan be obtained in the front face direction, (2) that a high luminancedistribution can be implemented in a direction within a predeterminedangular field of view, (3) that the second order transmission light canbe suppressed, and (4) that the angular field of view can be expanded.

Now, results of a study regarding numerical values of the radius R ofcurvature of the distal end vertex, the conic constant K and theaspheric coefficients A, B, C . . .based on a peak luminancedistribution are described.

WORKING EXAMPLE 8

(Where K=−1)

A peak luminance distribution in response to a variation of the radius Rof curvature of the distal end vertex and the aspheric coefficient Aaccording to the expression (1) given hereinabove into which the conicconstant K=−1 was substituted was determined. FIG. 23 illustrates a peakluminance distribution in the case of the conic constant K=−1.

WORKING EXAMPLE 9

(Where K=−1.5)

A peak luminance distribution in response to a variation of the radius Rof curvature of the distal end vertex and the aspheric coefficient Aaccording to the expression (1) given hereinabove into which the conicconstant K=−1.5 was substituted was determined. FIG. 24 illustrates apeak luminance distribution in the case of the conic constant K=−1.5.

WORKING EXAMPLE 10

(Where K=−2)

A peak luminance distribution in response to a variation of the radius Rof curvature of the distal end vertex and the aspheric coefficient Aaccording to the expression (1) given hereinabove into which the conicconstant K=−2 was substituted was determined. FIG. 25 illustrates a peakluminance distribution in the case of K=−2.

WORKING EXAMPLE 11

(Where K=−5)

A peak luminance distribution in response to a variation of the radius Rof curvature of the distal end vertex and the aspheric coefficient Aaccording to the expression (1) given hereinabove into which the conicconstant K=−5 was substituted was determined. FIG. 26 illustrates a peakluminance distribution in the case of K=−5.

WORKING EXAMPLE 12

(Where K=−10)

A peak luminance distribution in response to a variation of the radius Rof curvature of the distal end vertex and the aspheric coefficient Aaccording to the expression (1) given hereinabove into which the conicconstant K=−10 was substituted was determined. FIG. 27 illustrates apeak luminance distribution in the case of K=−10.

WORKING EXAMPLE 13

(Where K=−15)

A peak luminance distribution in response to a variation of the radius Rof curvature of the distal end vertex and the aspheric coefficient Aaccording to the expression (1) given hereinabove into which the conicconstant K=−15 was substituted was determined. FIG. 28 illustrates apeak luminance distribution in the case of K=−15.

WORKING EXAMPLE 14

(Where K=−20)

A peak luminance distribution in response to a variation of the radius Rof curvature of the distal end vertex and the aspheric coefficient Aaccording to the expression (1) given hereinabove into which the conicconstant K=−20 was substituted was determined. FIG. 29 illustrates apeak luminance distribution in the case of K=−20.

Now, results of a study regarding the convex portions provided on therear face side of a lens sheet are described.

WORKING EXAMPLE 15

First, an elastic roll was produced in the following manner. A seamlesstube was formed by Ni plating, and a Cr plating process was performedfor the surface of the seamless tube. Thereafter, the plated Cr layerwas polished to 0.2 S to produce a seamless tube (hereinafter referredto as flexible sleeve) having a thickness of 340 microns. Then, theouter circumferential face of the flexible sleeve was processed with astainless steel material (SUS material).

Then, glass beads having a predetermined particle size (diameter) wereblasted into the flexible sleeve by a bead blast processing machineproduced by Fuji Manufacturing Co., Ltd. to form a concave and convexshape on the outer circumferential face of the flexible sleeve. It is tobe noted that the blasting angle was approximately 30° with respect to anormal line to the outer circumferential face of the flexible sleeve.

Then, an elastic member was adhered to a roll in which coolant can becirculated and the flexible sleeve was fitted on the elastic member toobtain an elastic roll having a configuration that cooling water iscirculated between the resilient member and the flexible sleeve. It isto be noted that, as the resilient member, nitrile-butadiene rubber(NBR) having a hardness of 85 degrees was used and the thickness thereofwas set to 20 mm. Further, the diameter Φ of the elastic roll was set to260 mm and the face length (width of the molding roll) was set to 450mm.

Then, the elastic roll obtained in this manner was attached to anextruded sheet precision molding apparatus, and a lens sheet wasproduced in the following manner.

First, the polycarbonate E2000R (by Mitsubishi Engineering-PlasticCorporation) was successively discharged from the T die until it wasnipped by the forming roll and the elastic roll, and then was wrappedaround the forming roll. It is to be noted that the surface temperatureof the forming roll was kept at Tg+35° C., and the surface temperatureof the lens sheet 14 was kept at 75° C. Here, Tg is the glass transitiontemperature of the polycarbonate resin.

Thereafter, the sheet was exfoliated from the forming roll by thecooling roll. It is to be noted that the surface temperature of thecooling water was kept at 115° C. Further, the speed of the takeupmachine was set to 7 m/min. From the foregoing, a lens sheet of 200 μmthick having the cylindrical lens elements provided on the front facethereof and having convex portions provided on the rear face thereof wasobtained.

The surface temperatures of the forming roll and the elastic rolldescribed above were measured at a position immediately preceding to thenip at which the measurement is least likely to be influenced by theheat of the resin while a sensor was contacted with the surface of therolls. Further, the surface temperature of the cooling roll was measuredat a position at which the sheet was nipped by the cooling roll and theforming roll while a sensor was contacted with the surface of thecooling roll. It is to be noted that, as the thermometers, a handy typedigital thermometer (by Chino Corporation, commodity name: ND511-KHN)was used, and as the sensors, a sensor for surface temperaturemeasurement (Anritsu Meter Co., Ltd., commodity name U-161K-00-D0-1) wasused.

WORKING EXAMPLES 16 to 25

Lens sheets were obtained in a similar manner as in the working example1 described hereinabove except that a concave and convex shape wasformed on an outer circumferential face of a flexible sleeve using glassbeads having a particle size (diameter) different among the differentworking examples and an elastic roll having the flexible sleeve providedthereon was used to form the rear face side of the sheet.

Then, evaluation of the number of convex portions provided on the rearface side of the lens sheets of the working examples 15 to 25 obtainedin such a manner as described above, the distance between the convexportions, the ten-point average roughness, the height of the convexportions at which the convex portion area occupies 1%, the dynamiccoefficient of friction, the front face luminance relative value, thesliding test and the external appearance blurring was conducted.

Evaluation of the Number of Convex Portions

The rear face of the lens sheets was measured by a three-dimensionalmeasuring instrument (by Kosaka Ltd., commodity name: E4100). Then, themeasured surface shape was subject to oblique arithmeticoperation-correction of a measurement oblique face by the least squaresmethod to obtain an average central plane (JIS B0601-1994). Thereafter,the number of convex portions having a height equal to or greater than0.20 μm from the average central face was calculated.

Evaluation of the Distance between Convex Portions

An average distance between those convex portions having a height of 0.2μm from the average central plane described above was determined.

Evaluation of the Ten-Point Average Roughness

Further, the differences between five greatest heights and five greatestvalley heights from the average central plane described above wereaveraged to calculate the ten-point average roughness SRz.

Evaluation of the Height of Those Convex Portions at Which the ConvexPortion Area Occupies 1%

The height from a certain central plane to a cutting plane along whichthe convex portions were cut in parallel to the central plane when,within a projection range from a normal direction to the central plane,the ratio of the total area of the cross sections of the convex portionswas 1% with respect to the projection area was determined. The height atwhich the sectional area exhibited the area ratio of 1% (5,000 μm²) wasdetermined within a range of 1,000 μm×500 μm.

Evaluation of the Dynamic Coefficient of Friction

A surface measuring instrument (by Shinto Scientific Co., Ltd.,commodity name: Type-22) was used to measure the friction of the lenssheet rear face side with respect to the diffusion sheet BS702 by Keiwaas an object of sliding motion with a load of 200 g.

Evaluation of the Front Face Luminance Relative Value

In order to evaluate actual machine characteristics, a lens sheet wasmounted on a 19-inch TV (television) set on the market manufactured bySony. In particular, a diffuser for mixture of light and non-uniformityelimination and a lens sheet of a working example were mountedsuccessively on a unit in which a cold cathode fluorescent tube (CCFL)was accommodated to form a backlight system, and a liquid crystal panelwas mounted on the backlight system to obtain a liquid crystal displayapparatus. Then, the front face luminance of the liquid crystal displayapparatus was measured by means of the CS-1000 by Konica Minolta.

Then, a lens sheet produced in a similar manner to a working exampleexcept that the formation of convex portions on the rear face side wasomitted was mounted similarly on a 19-inch TV receiver on the marketmanufactured by Sony to obtain a liquid crystal display apparatus, andthe front face luminance of the liquid crystal display apparatus wasmeasured by means of the CS-1000 by Konica Minolta.

Then, the relative value of the front face luminance of the formerliquid crystal display apparatus was determined with reference to thefront face luminance of the latter liquid crystal display apparatus.

Evaluation by a Sliding Test

A surface measuring instrument (by Shinto Scientific Co., Ltd.,commodity name: Heiden Type-22) was used to perform a sliding testbetween the rear surface of a lens sheet and a diffuser (MS resin). Itis to be noted that the load was set to 200 g and the number of times ofreciprocating sliding movement was set to 100. Then, a scar of thesliding face was observed through a backlight unit for observation of aphotographic negative on the market, and the degree of the scar wasevaluated into three stages including (1) that a few scars exist, (2)that several scars exit and (3) that scars exist over an overall area.

Evaluation of the External Appearance Blurring

When a lens sheet was mounted on a 19-inch TV receiver on the marketmanufactured by Sony to observe a liquid crystal panel in a similarmanner as in the case of the evaluation of the front face luminancerelative value described above, it was confirmed by visual observationwhether or not a blurring state on an external appearance (ununiformityin luminance) was observed while the observation direction wassuccessively changed.

WORKING EXAMPLES 26 to 36

Lens sheets having no lenses provided on the front face side and havinga concave and convex shape provided on the rear face side were obtainedin a similar manner as in the working examples 15 to 25 describedhereinabove except that a forming roll having a mirror face-like moldingface was prepared and used to prepare a lens sheet.

Evaluation of the Haze

The haze (degree of cloudiness) of the lens sheets of the workingexamples 26 to 36 obtained in such a manner as described above wasmeasured using a haze meter (by Murakami Color Research Laboratory,commodity name: HM-150).

Evaluation of the Average Inclination Gradient

The average inclination gradient of the lens sheets of the workingexamples 22 to 32 obtained in such a manner as described above wasdetermined.

The average inclination gradient is given by the following expressionwhere the rectangular coordinate axes of the X and Y axes are placed onthe center of a roughness curve and an axis perpendicular to the centerplane is set as the Z axis and the roughness curve is represented by f(x, y) while the size of the reference plane is represented by Lx andLy:

${\delta\; a} = {\frac{1}{S_{M}}{\int_{0}^{Lx}{\int_{0}^{Ly}{\sqrt{( \frac{\delta\; f}{\delta\; x} )^{2} + ( \frac{\delta\; f}{\delta\; y} )^{2}}{\mathbb{d}x}{\mathbb{d}y}}}}}$S_(M) = Lx × Ly

FIGS. 30 and 31 illustrate results of the evaluation obtained in such amanner as described above. It is to be noted that numerals in the columnof a decision result of the sliding test indicates the followingdecision results.

1: scars exist over an overall area, 2: several scars exist, 3: a fewscars exist

FIG. 32 is a graph illustrating a relationship between the number ofthose convex portions equal to or greater than 0.2 μm and the luminancerelative value. FIG. 33 is a graph illustrating a relationship betweenthe number of those convex portions equal to or greater than 0.2 μm andthe external appearance blurring. FIG. 34 is a graph illustrating arelationship between the distance between those convex portions equal toor greater than 0.2 μm and the luminance relative value. FIG. 35 is agraph illustrating a relationship between the distance between thoseconvex portions equal to or greater than 0.2 μm and the sliding testresult. FIG. 36 is a graph illustrating a relationship between thenumber of those convex portions equal to or greater than 0.2 μm and theexternal appearance blurring. FIG. 37 is a graph illustrating arelationship between the ten-point average roughness SRz and theluminance relative value. FIG. 38 is a graph illustrating a relationshipbetween the ten-point average roughness SRz and the sliding test result.FIG. 39 is a graph illustrating a relationship between the height atwhich the convex portion area occupies 1% and the luminance relativevalue. FIG. 40 is a graph illustrating a relationship between the heightat which the convex portion area occupies 1% and the sliding testresult. FIG. 41 is a graph illustrating a relationship between the hazeand the luminance relative value. FIG. 42 is a graph illustrating arelationship between the average inclination gradient and the luminancerelative value.

From the evaluation results of FIGS. 30 to 41, the followings can berecognized.

Evaluation Results of the Number of Convex Portions

From the evaluation result of the external appearance blurring (refer toFIG. 33), it can be recognized that, by setting the density of convexportions equal to or greater than 70/mm², the external appearanceblurring caused by interference of the diffuser provided on the rearface side of a lens sheet with the flat face portion can be improved.

Further, from the evaluation result of the front face luminance relativevalue (refer to FIG. 32), it can be recognized that, by setting thedensity of convex portions equal to or lower than 400/mm², a drop of theluminance of a liquid crystal display apparatus caused by provision ofthe convex portions on the rear face side of a lens sheet can besuppressed.

Evaluation Results of the Distance Between the Convex Portions

From the evaluation result of the front face luminance relative value(refer to FIG. 34), it can be recognized that, by setting the averagedistance between the convex portions equal to or more than 50 μm, a dropof the luminance of a liquid crystal display apparatus caused byprovision of the convex portions on the rear face side of a lens sheetcan be suppressed.

Further, from the evaluation result of the sliding test and theevaluation result of the external appearance blurring (refer to FIGS. 35and 36), it can be recognized that, by setting the average distancebetween the convex portions equal to or smaller than 120 μm, formationof scars on the surface of the diffuser by the rear face of the lenssheet can be prevented and the external appearance blurring caused byinterference of the diffuser provided on the rear face side of the lenssheet with the flat face portion can be improved.

Evaluation Results of the Ten-Point Average Roughness

From the evaluation result of the sliding test and the evaluation resultof the external appearance blurring (refer to FIGS. 30 and 38), it canbe recognized that, by setting the ten-point average roughness SRz ofthe convex portions equal to or higher than 1 μm, formation of scars onthe surface of the diffuser by the rear face of the lens sheet can beprevented and the external appearance blurring caused by interference ofthe diffuser provided on the rear face side of the lens sheet with theflat face portion can be improved.

From the evaluation result of the front face luminance relative value(refer to FIG. 37), it can be recognized that, by setting the ten-pointaverage roughness SRz of the convex portions equal to or less than 15μm, a drop of the luminance of a liquid crystal display apparatus causedby provision of the convex portions on the rear face side of a lenssheet can be suppressed.

Evaluation Results of the Height of the Convex Portions at Which the 1%Area is Exhibited

From the evaluation result of the sliding test and the evaluation resultof the external appearance blurring (refer to FIGS. 30 and 40), it canbe recognized that, by setting the height of the convex portions atwhich the convex portion area occupies 1% equal to or greater than 1 μm,formation of scars on the surface of the diffuser by the rear face ofthe lens sheet can be prevented and the external appearance blurringcaused by interference of the diffuser provided on the rear face side ofthe lens sheet with the flat face portion can be improved.

Further, from the evaluation result of the front face luminance relativevalue (refer to FIG. 39), it can be recognized that, by setting theheight of the convex portions at which the convex portion area occupies1% equal to or smaller than 7 μm, a drop of the luminance of a liquidcrystal display apparatus caused by provision of the convex portions onthe rear face side of a lens sheet can be suppressed.

Evaluation Result of the Haze

From the evaluation result of the front face luminance relative value(refer to FIG. 41), it can be recognized that, by setting the haze of alens sheet in a state wherein no lens pattern is formed equal to orlower than 60%, a drop of the luminance of a liquid crystal displayapparatus caused by provision of the convex portions on the rear faceside of a lens sheet can be suppressed. Further, it can be recognizedthat, by setting the haze of a lens sheet in a state wherein no lenspattern is formed equal to or lower than 20%, a drop of the luminance ofa liquid crystal display apparatus caused by provision of the convexportions on the rear face side of a lens sheet can be furthersuppressed.

Evaluation Result of the Average Inclination Gradient

From the evaluation result of the front face luminance relative value(refer to FIG. 42), it can be recognized that, by setting the averageinclination gradient δa in a state wherein no lens pattern is formedequal to or lower than 0.25 (rad), a drop of the luminance of a lenssheet can be suppressed.

As described above, by providing convex portions on the rear face of alens sheet, improvement in the external appearance blurring andimprovement in the mechanical characteristics such as a slidingcharacteristic can be achieved without degrading the luminance. It isconsidered that the reduction of the external appearance blurring iscaused by prevention of sticking to the diffuser by the convex portions.Further, it is considered that the improvement of the sliding testcharacteristic is caused by reduction of the friction upon sliding bythe convex portion components.

The present invention is not restricted to the working examples of thepresent invention described above, but various modifications andapplications can be made without departing from the spirit and scope ofthe present invention. For example, a similar improvement effect of thefront face luminance can be anticipated by disposition above a lightguide plate.

Further, similar effects can be exhibited even where the lens sheet isdisposed on the light emitting side face of the backlight from a lightguide plate within a display unit which utilizes liquid crystal or evenwhere the lens sheet is disposed on the incidence side front portion ofa liquid crystal display panel.

Further, while, in the working examples described above, a case whereinone lens sheet is provided in a backlight and a liquid crystal displayapparatus is described as an example, a plurality of lens sheets may beprovided.

Further, the backlight 1 is not limited to the one working exampledescribed hereinabove, but may be configured such that it includes thelens sheet 14 above a light guide plate, an EL (Electro Luminescence)light emitting face, a planar light emitting CCFL (Cold CathodeFluorescent Tube) or some other light source. Also in this instance, afront face luminance improvement effect similar to that of the oneembodiment described hereinabove can be achieved.

While, in the one working example described hereinabove, a case whereina lens sheet is produced by a melt extrusion method is described, thelens sheet may be produced by a thermal press method. For example, abead blasting or sand blasting machine on the market is used and thetype of particles, particle size and shot speed are varied to produce aconcave and convex shape on the face of the press plate for forming therear face. A lens sheet can be obtained by vacuum thermoforming athermoplastic resin using the press plate obtained in this manner and apress plate on which a concave and convex shape for forming cylindricallens elements.

A production method of the lens sheet by a melt extrusion method isdescribed more particularly.

First, glass beads having a particle size are blasted into an SUSmaterial plate on the market having a thickness t of, for example, t=1mm by a bead blast processing machine by Fuji Manufacturing Co., Ltd. toproduce a press plate for forming the rear face side of a lens sheet.Thereupon, the blasting angle is set, for example, to an angle ofapproximately 30° with respect to a perpendicular direction to the SUSmaterial plate.

Then, a sheet of a thickness t of t=200 μm made of, for example,polycarbonate or the like is sandwiched between the press sheet obtainedin such a manner as described above and a metal mold having a lenspattern provided thereon and is press formed for 10 minutes at 170°C.×10 kg/cm², for example, by a vacuum thermal press machine, whereafterit is cooled to a room temperature. An object lens sheet is obtainedthereby.

Further, while, in the one working example described hereinabove, anexample wherein the convex portions 16 are provided on the cylindricalface of the elastic roll 24 to form the convex portions 16 on the rearface of the lens sheet 14 is described as an example, the shape of thecylindrical face of the elastic roll 24 is not limited to this. Forexample, where the rear face of the lens sheet 14 is to be formed as aflat face, the cylindrical face of the elastic roll 24 may be formed asa mirror face.

Further, in the one working example described hereinabove, the liquidcrystal display apparatus may further includes a protect sheet forpreventing damage to the lens sheet 14. One of principal faces of theprotect sheet is formed as a flat face while the other principal face isformed as a concave and convex face having convex portions providedthereon similarly to the rear face of the lens sheet 14. Where convexportions are to be formed only on one face of the protect sheet, theprotect sheet is provided on the liquid crystal display apparatus insuch a manner that the face of the protect sheet on which the convexportions are provided is opposed to the light sources 12. It is to benoted that the convex portions may be provided on the opposite faces ofthe protect sheet.

The protect sheet may be provided, for example, between the lens sheet14 and the reflection type polarizer 18. Or, a protect sheet may beprovided in place of the reflection type polarizer 18.

It should be understood that various changes and modifications to thepresently preferred embodiments described herein will be apparent tothose skilled in the art. Such changes and modifications can be madewithout departing from the spirit and scope of the present invention andwithout diminishing its intended advantages. It is therefore intendedthat such changes and modifications be covered by the appended claims.

1. An optical sheet comprising a plurality of lens elements providedsuccessively in a row on one of principal faces of said optical sheet,wherein if a Z axis is taken in parallel to a normal line direction tosaid optical sheet and an X axis is taken in a direction of the row ofsaid lens elements, a cross sectional shape in the XZ plane of each ofsaid lens elements has a hyperboloidal or paraboloidal structure inwhich an entire surface of each of said lens elements satisfies thefollowing expression:Z=X ²/(R+√(R ²−(1+K)X ²))+AX ⁴ +BX ⁵ +CX ⁶ where R is the radius ofcurvature of a distal end vertex, K is a conic constant, and A, B, C areaspheric coefficients, and wherein the radius R of curvature, the conicconstant K and the aspheric coefficients A, B, C satisfy the followingnumerical ranges: R≧0, K≦−1, 0<A<10⁻³, and 0≦B, C<10⁻³.
 2. The opticalsheet according to claim 1, wherein the radius R of curvature, the conicconstant K and the aspheric coefficients A, B, C satisfy the followingnumerical ranges: 0<R≦72 −15<K≦−1 R−K≧5 0≦A, B, C<10⁻³.
 3. The opticalsheet according to claim 1, wherein the radius R of curvature, the conicconstant K and the aspheric coefficients A, B, C satisfy the followingnumerical ranges: 0<R≦30 −15<K≦−1 R−K≧5 0≦A, B, C<10⁻³.
 4. The opticalsheet according to claim 1, further comprising convex portions having aheight equal to or greater than 0.20 μm from an average central plane onthe principal face side opposite to the principal face on which saidlens elements are provided, wherein the density of said convex portionsis equal to or higher than 70 /mm² but equal to or lower than 500 /mm².5. The optical sheet according to claim 1, further comprising convexportions having a height equal to or greater than 0.20 μm from anaverage central plane on the principal face side opposite to theprincipal face on which said lens elements are provided, wherein theaverage distance between said convex portions is equal to or greaterthan 50 μm but equal to or smaller than 120 μm.
 6. The optical sheetaccording to claim 1, further comprising convex portions on theprincipal face side opposite to the one principal face on which saidlens elements are provided, wherein said convex portions are providedsuch that, in a state wherein said lens elements are not formed, thecloudiness degree of said optical sheet is equal to or lower than 60%.7. The optical sheet according to claim 1, further comprising convexportions on the principal face side opposite to the one principal faceon which said lens elements are provided, wherein said convex portionsare provided such that, in a state wherein said lens elements are notformed, the cloudiness degree of said optical sheet is equal to or lowerthan 20%.
 8. The optical sheet according to claim 1, further comprisingconvex portions on the principal face side opposite to the one principalface on which said lens elements are provided, wherein the ten-pointaverage roughness SRz of said convex portions is equal to or higher than1 μm but equal to or lower than 15 μm.
 9. The optical sheet according toclaim 1, further comprising convex portions on the principal face sideopposite to the one principal face on which said lens elements areprovided, wherein the height of said convex portions at which the convexportion area occupies 1% is equal to or greater than 1 μm but equal toor smaller than 7 μm.
 10. The optical sheet according to claim 1,further comprising convex portions on the principal face side oppositeto the one principal face on which said lens elements are provided,wherein the average inclination gradient of the face on the side onwhich said convex portions are provided is equal to or lower than 0.25.11. The optical sheet according to claim 1, further comprising convexportions provided on the principal face side opposite to the principalface on which said lens elements are provided.
 12. The optical sheetaccording to claim 1, wherein the optical sheet including the lenselements is a single-layer element formed by thermal transfer of adesired shape to the sheet.
 13. The optical sheet according to claim 1,wherein the optical sheet comprises a transparent thermoplastic resin.14. The optical sheet according to claim 13, wherein the transparentthermoplastic resin includes at least one release agent in an amountbetween about 0.02% and 0.04% by weight of the transparent thermoplasticresin.
 15. The optical sheet according to claim 13, wherein thetransparent thermoplastic resin includes at least one ultravioletabsorbing agent or light stabilizer in an amount between about 0.02% and0.40% by weight of the transparent thermoplastic resin.
 16. A backlight,comprising: a light source for emitting illumination light; and anoptical sheet for raising the directivity of the illumination lightemitted from said light source, said optical sheet comprising, on theillumination light emission side thereof, a plurality of lens elementsprovided successively in a row, wherein if a Z axis is taken in parallelto a normal line direction to said optical sheet and an X axis is takenin a direction of the row of said lens elements, a cross sectional shapein the XZ plane of each of said lens elements has a hyperboloidal orparaboloidal structure in which an entire surface of each of said lenselements satisfies the following expression:Z=X ²/(R+√(R ²−(1+K)X ²))+AX ⁴ +BX ⁵ +CX ⁶ where R is the radius ofcurvature of a distal end vertex, K is a conic constant, and A, B, C areaspheric coefficients, and wherein the radius R of curvature, the conicconstant K and the aspheric coefficients A, B, C satisfy the followingnumerical ranges: R≧0, K≦−1, 0<A<10⁻³, and 0≦B, C<10⁻³.
 17. A liquidcrystal display apparatus, comprising: a light source for emittingillumination light; an optical sheet for raising the directivity of theillumination light emitted from said backlight, said optical sheetcomprising, on the illumination light emission side thereof, a pluralityof lens elements provided successively in a row; and a liquid crystalpanel for displaying an image based on the illumination light emittedfrom said optical sheet, wherein if a Z axis is taken in parallel to anormal line direction to said optical sheet and an X axis is taken in adirection of the row of said lens elements, a cross sectional shape inthe XZ plane of each of said lens elements has a hyperboloidal orparaboloidal structure in which an entire surface of each of said lenselements satisfies the following expression:Z=X ²/(R+√(R ²−(1+K)X ²))+AX ⁴ +BX ⁵ +CX ⁶ where R is the radius ofcurvature of a distal end vertex, K is a conic constant, and A, B, C areaspheric coefficients, and wherein the radius R of curvature, the conicconstant K and the aspheric coefficients A, B, C, satisfy the followingnumerical ranges: R≧0, K≦−1, 0<A<10⁻³, and 0≦B, C<10⁻³.